# Proof sin(10) is irrational.

## Homework Statement

Prove $\sin{10}$, in degrees, is irrational.

## Homework Equations

None, got the problem as is.

Im kinda lost.

STEMucator
Homework Helper

## Homework Statement

Prove $\sin{10}$, in degrees, is irrational.

## Homework Equations

None, got the problem as is.

## The Attempt at a Solution

Im kinda lost.

Okay, are you familiar with proof by contradiction?

Start by contradicting the statement :

Suppose that sin(10) is irrational.

Dick
Homework Helper

## Homework Statement

Prove $\sin{10}$, in degrees, is irrational.

## Homework Equations

None, got the problem as is.

## The Attempt at a Solution

Im kinda lost.

Let x=sin(10). You'll want to find a polynomial x satisfies and show it has no rational root. Hint: sin(30)=1/2=sin(10+10+10).

I should suppose sin(10) is rational, if i am to contradict the statement, shouldnt i?

jedishrfu
Mentor
yes and that means that sin(10) can be represented by the ratio of two integers a and b sin(10) = a/b

next step...

Dick